Question

How do you factor `12x^2 - xy - y^2`?

Answer 1

`(y-4x)(y+3x)`

Explanation:

One way of doing that is by appealing to the homogeneity so making `y=lambda x` and substituting

`12x^2-xy-y^2=(12-lambda-lambda^2)x^2` or

`(lambda+4)(lambda-3)x^2=(lambda x-4x)(lambda x+3x) = (y-4x)(y+3x)`